Does the Vector Math Normalize operation use the second input?
Input 2 is not used, manual is wrong, I guess. Links to the source code for the node are below, you can clearly see input 2 is never called when in normalize mode. 

SVM: https://developer.blender.org/diffusion/B/browse/master/intern/cycles/kernel/svm/svm_math_util.h

OSL: https://developer.blender.org/diffusion/B/browse/master/intern/cycles/kernel/shaders/node_vector_math.osl